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A generalization of \(\beta\)-compact space and \(\beta\)-perfect functions. (English) Zbl 1456.54005

Summary: In this paper, we have introduced a new covering space, namely \(\beta J\)-space in terms of \(\beta\)-closed sets [M. E. Abd El-Monsef et al., Bull. Fac. Sci., Sect. A, Assiut Univ. 12, 77–90 (1983; Zbl 0577.54008)] and \(\beta\)-compactness [M. E. Abd El-Monsef et al., “Some generalized forms of compactness and closedness”, Delta J. Sci. 9, No. 2, 257–269 (1985)] along with its several properties. We have found several characterizations of \(\beta J\)-spaces via \(\beta\)-open sets, \(\beta\)-frontiers. Further, we have introduced two new functions \(\beta\)-perfect function and \(\beta\)-boundary \(\beta\)-perfect function between two topological spaces along with their some characterizations via filters, \(\beta\)-open covers of the domain spaces of the functions. We have also achieved a characterization of \(\beta\)-compact space via \(\beta\)-perfect functions. Further, we have investigated some applications of these two new functions on \(\beta\)-compact spaces and \(\beta J\)-spaces.

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D30 Compactness
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54E55 Bitopologies
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)

Citations:

Zbl 0577.54008
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